15 Astronomical and Geophysical Factors of the Perturbed Chandler Wobble …
209
oscillations of the Earth pole coordinates x
p , y
p ) in one of the coordinates and the
lowest level in the other. The calculations were carried out in a 5° increment.
The resulted graphs show the differences in the harmonics amplitudes of the highfrequency regions. The logarithmic scale for amplitudes was used along the ordinate
axis of the graphs. The graphs show that the lowest level of noise (in the frequency
range from 5 to 40 cycles per year) is observed at the coordinate x
, rotated by an
angle of about 40° to the east of Greenwich. The highest level of high-frequency
oscillations approximately corresponds to the y
axis, which preserves the direction
orthogonal to the x
axis, although the maximum is less explicit than the minimum
along the x
axis.
The correspondence of the positions of the axes x
, y
to the distribution of water
mass over the Earth’s surface can be shown visually using simple reasoning. First,
we determine the dependence of the total ocean surface ratio to the land surface on
longitude. To obtain accurate results, topographic data should be used, followed by
their integration over latitude. However, since a high accuracy is not required for a
qualitative analysis, we can consider a more original method, which is quite suitable
for the purposes of this work. In [19], the results of broadband photometry of the
Earth were presented according to the data from the Deep Impact spacecraft operating
under the EPOXI mission, and the dependence of the land surface distribution on the
longitude was constructed on the basis of light curves. Denote by k(θ ) the share of
the ocean surface at longitude θ is defined by Eq. 15.8.
k(θ ) =
Ocean Surface at longitude θ
Earth Surface at longitude θ
(15.8)
Variations in the centrifugal moments of inertia J x z , J y z have a perturbing effect
on the Earth pole oscillatory process. Since the centrifugal moments of inertia characterize the masses distribution relative to the coordinate planes x
z, y
z, their sensitivity is higher to the motion of the moving medium on the Earth’s surface that is
located closer to the corresponding plane. Then they will have the greatest sensitivity
to tangential displacements in a sector bounded by two meridians and containing a
plane with respect to which the moments of inertia are calculated. In this case, the
motion of particles on the surface bounded by such a sector occurs in tangential
directions, but their latitude is unknown, since the introduced coefficient k(θ ) as an
integral value does not depend on latitude and there is no resolution on latitude.
Now we choose two sectors that are symmetrical with respect to the coordinate
planes x
z, y
z with angles at the vertex 2θ 0 . When the axes are rotated, the selected
sectors will also rotate. If the moving medium is evenly distributed over the surface
of the hemisphere (e.g., for x
> 0) and is “frozen” on the opposite hemisphere, then
the particle motion on the surface bounded by such a sector determine approximately
100 sin θ 0 % of the variable part for the centrifugal moments of inertia (at θ 0 = π/2
the sector becomes a hemisphere). For an unevenly distributed medium, this value
can differ and the smaller the angle θ 0 ∈ (0, π/2], the larger the difference. But on
the other hand, the larger the angle θ 0 (i.e., the larger the area of the surface under
consideration), the greater the uncertainty of the correspondence between the ocean
209
oscillations of the Earth pole coordinates x
p , y
p ) in one of the coordinates and the
lowest level in the other. The calculations were carried out in a 5° increment.
The resulted graphs show the differences in the harmonics amplitudes of the highfrequency regions. The logarithmic scale for amplitudes was used along the ordinate
axis of the graphs. The graphs show that the lowest level of noise (in the frequency
range from 5 to 40 cycles per year) is observed at the coordinate x
, rotated by an
angle of about 40° to the east of Greenwich. The highest level of high-frequency
oscillations approximately corresponds to the y
axis, which preserves the direction
orthogonal to the x
axis, although the maximum is less explicit than the minimum
along the x
axis.
The correspondence of the positions of the axes x
, y
to the distribution of water
mass over the Earth’s surface can be shown visually using simple reasoning. First,
we determine the dependence of the total ocean surface ratio to the land surface on
longitude. To obtain accurate results, topographic data should be used, followed by
their integration over latitude. However, since a high accuracy is not required for a
qualitative analysis, we can consider a more original method, which is quite suitable
for the purposes of this work. In [19], the results of broadband photometry of the
Earth were presented according to the data from the Deep Impact spacecraft operating
under the EPOXI mission, and the dependence of the land surface distribution on the
longitude was constructed on the basis of light curves. Denote by k(θ ) the share of
the ocean surface at longitude θ is defined by Eq. 15.8.
k(θ ) =
Ocean Surface at longitude θ
Earth Surface at longitude θ
(15.8)
Variations in the centrifugal moments of inertia J x z , J y z have a perturbing effect
on the Earth pole oscillatory process. Since the centrifugal moments of inertia characterize the masses distribution relative to the coordinate planes x
z, y
z, their sensitivity is higher to the motion of the moving medium on the Earth’s surface that is
located closer to the corresponding plane. Then they will have the greatest sensitivity
to tangential displacements in a sector bounded by two meridians and containing a
plane with respect to which the moments of inertia are calculated. In this case, the
motion of particles on the surface bounded by such a sector occurs in tangential
directions, but their latitude is unknown, since the introduced coefficient k(θ ) as an
integral value does not depend on latitude and there is no resolution on latitude.
Now we choose two sectors that are symmetrical with respect to the coordinate
planes x
z, y
z with angles at the vertex 2θ 0 . When the axes are rotated, the selected
sectors will also rotate. If the moving medium is evenly distributed over the surface
of the hemisphere (e.g., for x
> 0) and is “frozen” on the opposite hemisphere, then
the particle motion on the surface bounded by such a sector determine approximately
100 sin θ 0 % of the variable part for the centrifugal moments of inertia (at θ 0 = π/2
the sector becomes a hemisphere). For an unevenly distributed medium, this value
can differ and the smaller the angle θ 0 ∈ (0, π/2], the larger the difference. But on
the other hand, the larger the angle θ 0 (i.e., the larger the area of the surface under
consideration), the greater the uncertainty of the correspondence between the ocean